{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T14:12:20Z","timestamp":1785420740689,"version":"3.56.0"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T00:00:00Z","timestamp":1778457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Hulunbuir University","award":["2024BSJJ16"],"award-info":[{"award-number":["2024BSJJ16"]}]},{"name":"Hulunbuir University","award":["2022BS01"],"award-info":[{"award-number":["2022BS01"]}]},{"name":"Hulunbuir University","award":["2024BSJJ05"],"award-info":[{"award-number":["2024BSJJ05"]}]},{"award":["2024BSJJ16"],"award-info":[{"award-number":["2024BSJJ16"]}],"id":[{"id":"https:\/\/ror.org\/02vx41k98","id-type":"ROR","asserted-by":"publisher"}]},{"award":["2022BS01"],"award-info":[{"award-number":["2022BS01"]}],"id":[{"id":"https:\/\/ror.org\/02vx41k98","id-type":"ROR","asserted-by":"publisher"}]},{"award":["2024BSJJ05"],"award-info":[{"award-number":["2024BSJJ05"]}],"id":[{"id":"https:\/\/ror.org\/02vx41k98","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>This paper proposes a multi-strategy improved pied kingfisher optimizer (MSIPKO), a novel metaheuristic algorithm designed to address constrained optimization problems (COPs). COPs are widely encountered in engineering and industrial applications and are characterized by complex constraints that restrict the feasible solution space and often lead to multiple local optima. To enhance the performance of the original pied kingfisher optimizer (PKO), three strategies are incorporated: (i) a reverse differential crossover mechanism to improve global exploration and maintain population diversity; (ii) an enhanced diving-fishing operator to strengthen local exploitation; and (iii) an improved commensalism phase to enrich search directions and increase robustness. The performance of MSIPKO is evaluated on 12 benchmark functions from the IEEE Congress on Evolutionary Computation 2006 (CEC 2006) test suite and six classical engineering optimization problems. Experimental results demonstrate that MSIPKO outperforms several state-of-the-art algorithms in terms of optimization accuracy, convergence speed, and stability, particularly for high-dimensional, nonlinear, and multi-constrained problems. Moreover, MSIPKO achieves superior or comparable solutions with fewer function evaluations, indicating its high efficiency and adaptability. These results confirm that MSIPKO is a promising tool for solving complex real-world constrained optimization problems. Future work will focus on extending the proposed algorithm to multi-objective and large-scale optimization scenarios.<\/jats:p>","DOI":"10.3390\/biomimetics11050335","type":"journal-article","created":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T17:17:42Z","timestamp":1778519862000},"page":"335","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Strategy Improved Pied Kingfisher Optimizer for Solving Constrained Optimization Problems"],"prefix":"10.3390","volume":"11","author":[{"given":"Hongmei","family":"Bai","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Hulunbuir University, Hailar 021008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Taosuo","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Engineering, Hulunbuir University, Hailar 021008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8017-5497","authenticated-orcid":false,"given":"Jianfu","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Engineering, Hulunbuir University, Hailar 021008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Na","family":"Ta","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence and Big Data, Hulunbuir University, Hailar 021008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"161745","DOI":"10.1109\/ACCESS.2021.3133579","article-title":"A modification of the imperialist competitive algorithm with hybrid methods for constrained optimization problems","volume":"9","author":"Luo","year":"2021","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1109\/TSMCA.2011.2162498","article-title":"Constrained multiple-swarm particle swarm optimization within a cultural framework","volume":"42","author":"Moayed","year":"2012","journal-title":"IEEE Trans. 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